The orexins (hypocretins) comprise two neuropeptides produced in the hypothalamus: the orexin A (OX-A) (a 33 amino acid peptide) and the orexin B (OX-B) (a 28 amino acid peptide) (Sakurai T. et al., Cell, 1998, 92, 573-585). Orexins are found to stimulate food consumption in rats suggesting a physiological role for these peptides as mediators in the central feedback mechanism that regulates feeding behaviour. Orexins regulate states of sleep and wakefulness opening potentially novel therapeutic approaches for narcoleptic or insomniac patients. Orexins have also been indicated as playing a role in arousal, reward, learning and memory. Two orexin receptors have been cloned and characterized in mammals. They belong to the super family of G-protein coupled receptors (7-transmembrane spanning receptor) (Sakurai T. et al., Cell, 1998, 92, 573-585): the orexin-1 receptor (OX1R or HCTR1) is more selective for OX-A than OX-B and the orexin-2 receptor (OX2R or HCTR2) binds OX-A as well as OX-B. A recent study shows that activation of OX1R by orexin can promote robust in vitro and in vivo apoptosis in colon cancer cells even when they are resistant to the most commonly used drug in colon cancer chemotherapy (Voisin T, El Firar A, Fasseu M, Rouyer-Fessard C, Descatoire V, Walker F, Paradis V, Bedossa P, Henin D, Lehy T, Laburthe M. Aberrant expression of OX1 receptors for orexins in colon cancers and liver metastases: an openable gate to apoptosis. Cancer Res. 2011 May 1; 71(9):3341-51). In particular, it was shown that OX1R promotes apoptosis in the cancer cell lines through a mechanism which is not related to Gq-mediated phospholipase C activation and cellular calcium transients. Orexins induce indeed tyrosine phosphorylation of 2 tyrosine-based motifs in OX1R, ITIM and ITSM, resulting in the recruitment of the phosphotyrosine phosphatase SHP-2, the activation of which is responsible for mitochondrial apoptosis (Voisin T, El Firar A, Rouyer-Fessard C, Gratio V, Laburthe M. A hallmark of immunoreceptor, the tyrosine-based inhibitory motif ITIM, is present in the G protein-coupled receptor OX1R for orexins and drives apoptosis: a novel mechanism. FASEB J. 2008 Jun.; 22(6):1993-2002.; El Firar A, Voisin T, Rouyer-Fessard C, Ostuni M A, Couvineau A, Laburthe M. Discovery of a functional immunoreceptor tyrosine-based switch motif in a 7-transmembrane-spanning receptor: role in the orexin receptor OX1R-driven apoptosis. FASEB J. 2009 Dec.; 23(12):4069-80. doi: 10.1096/fj.09-131367. Epub 2009 Aug. 6). Remarkably, all primary colorectal tumors regardless of their localization and Duke's stages expressed OX1R while adjacent normal colonocytes as well as control normal tissues were negative. Besides, expression of OX1R has been recently confirmed in pancreatic cancer, hepatocarcimomas, and advanced prostate cancer. Accordingly the prior art supports that OX1R is an Achilles's heel of cancers (even chemoresistance) and suggests that OX1R is a relevant target for cancer therapy. However, antibodies against OX1R that are capable of promoting apoptosis of cancer cells have never been described in the prior art.